Signal recording parameters (EE)

What (complete) set of sampling and filtering parameters would you choose to record a signal from a high speed pressure sensor if you wanted to accurately determine its power spectrum below 35 kHz with a resolution of 0.5 Hz?

The sampling rate must satisfy the criterion of no aliasing. If the frequency spread of interest is 0 - 35 KHz, what is the minimum sampling frequency?

You realize I assume that this is a DFT problem. So how many time samples N would you need to achieve 0.5 Hz resolution of the 0 - 35 KHz signal? It's not the formula you gave above for freq. resolution.

You then get N/2 + 1 numbers representing the cosine component and another N/2 + 1 numbers representing the sine component of each harmonic of the fundamental frequency which is the resolution frequency. So what would be the power in each frequency component 0, 1/NT, 2/NT etc. where 1/T is the sampling frequency?

(You can also get complex frequency components. This is actually easier for determining power for each harmonic.)

I don't see the need for a reconstruction filter if all you want is the power spectrum.